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- Title
Lipschitz stratifications in power-bounded o-minimal fields.
- Authors
Halupczok, Immanuel; Yimu Yin
- Abstract
We propose to grok Lipschitz stratifications from a non-archimedean point of view and thereby show that they exist for closed definable sets in any power-bounded o-minimal structure on a real closed field. Unlike the previous approaches in the literature, our method bypasses resolution of singularities andWeierstraß preparation altogether; it transfers the situation to a non-archimedean model, where the quantitative estimates appearing in Lipschitz stratifications are sharpened into valuation-theoretic inequalities. Applied to a uniform family of sets, this approach automatically yields a family of stratifications which satisfy the Lipschitz conditions in a uniform way.
- Subjects
LIPSCHITZ spaces; ALGEBRAIC fields; VALUATION theory; SET theory; ARCHIMEDEAN property
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2018, Vol 20, Issue 11, p2717
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/823